Why we must demonstrate the electroweak theory to be renormalizable?

ndung200790

In general speaking,if the coupling constant is (mass) dimensionless then the quantum field theory is renormalizable.In electroweak theory the coupling constant g~e,so the coupling constant is dimensionless,then the electroweak theory(Weinberg-Salam theory) would be renormalizable.So I do not understand why in 1971(I have heard that) t' Hooft must demonstrate the Weinberg-Salam to be renormalizable.I also can not find in any text book the t'Hooft's demonstration,where can I find it?
Please forgive me if my question is not good question(I have to self-study the subject)

ndung200790

I have known that in electroweak theory we have to solve the anomaly problem.But I do not understand why the anomaly problem relates with the renormalization problem(divergent problem)

jarod765

In general proving that a theory is renormalizable is not an easy task. First you must make sure that any divergent integrals can be absorbed by a finite set of counter terms, you must properly fix the gauge while at the same time making sure that any non-physical degrees of freedom do not appear in physical calculations.

I do not quite remember what Thooft did but I do know one of his contributions was dimensional regularization which brought leaps and bounds on our abilities to do regularization in a Lorentz covariant way.

ndung200790

Thank jarod very much!

tom.stoer

The dimensional analysis gives you a hint on the structure of counter terms; it doesn't say anything regarding quantization anomalies which could arise in loop calculations. So one major step was to provide a regularization method which preserves the "physical anomaly structure" (triangle anomalies in chiral theories) and to study their cancellation w/o introducing "unphysical anomalies" which would arise e.g. in the unmodified Pauli–Villars regularization approach.

Hoogah

We do not need it to be renormalizable but we need it to be stable. That y we made it renormalizable.

ndung200790

So,is there any relation between anomalies and renormalization characteristic?

ndung200790

It seems that there is a close relation between Ward(Taylor) Identity and BPHZ theorem?